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In architecture and structural engineering, a truss is a structure comprising one or more triangular units constructed with straight slender members whose ends are connected at joints referred to as nodes. External forces and reactions to those forces are considered to act only at the nodes and result in forces in the members which are either tensile or compressive forces. Moments (torsional forces) are explicitly excluded because, and only because, all the joints in a truss are treated as revolutes.

A planar truss is one where all the members and nodes lie within a two dimensional plane, while a space truss has members and nodes extending into three dimensions.

Characteristics of trusses

A truss is composed of triangles because of the structural stability of that shape and design. A triangle is the simplest geometric figure that will not change shape when the lengths of the sides are fixed.In comparison, both the angles and the lengths of a square must be fixed for it to retain its shape.

The simplest form of a truss is one single triangle. This type of truss is seen in a framed roof consisting of rafters and a ceiling joist. Because of the stability of this shape and the methods of analysis used to calculate the forces within it, a truss composed entirely of triangles is known as a simple truss.

A planar truss lies in a single plane. Planar trusses are typically used in parallel to form roofs and bridges. A space truss is a three-dimensional framework of members pinned at their ends. A tetrahedron shape is the simplest space truss, consisting of six members which meet at four joints.

The depth of a truss, or the height between the upper and lower chords, is what makes it an efficient structural form. A solid girder or beam of equal strength would have substantial weight and material cost as compared to a truss. For a given span length, a deeper truss will require less material in the chords and greater material in the verticals and diagonals. An optimum depth of the truss will maximize the efficiency.

Truss types

There are two basic types of truss:

* The pitched truss, or common truss, is characterized by its triangular shape. It is most often used for roof construction. Some common trusses are named according to their web configuration. The chord size and web configuration are determined by span, load and spacing. * The parallel chord truss, or flat truss, gets its name from its parallel top and bottom chords. It is often used for floor construction.

A combination of the two is a truncated truss, used in hip roof construction. A metal plate-connected wood truss is a roof or floor truss whose wood members are connected with metal connector plates.

Pratt truss

Vierendeel Truss The Pratt truss was patented in 1844 by two Boston railway engineers; Caleb Pratt and his son Thomas Willis Pratt. The design uses vertical beams for compression and horizontal beams to respond to tension. What is remarkable about this style is that it remained popular even as wood gave way to iron, and even still as iron gave way to steel.

The Southern Pacific Railroad bridge in Tempe, Arizona is a 393 meter (1291 foot) long truss bridge built in 1912. The structure is composed of nine Pratt truss spans of varying lengths. The bridge is still in use today

Bow string roof truss

Named for its vicissitudal shape, thousands of bow strings were used during World War II for aircraft hangars and other military buildings.

King post truss

One of the simplest truss styles to implement, the king post consists of two angled supports leaning into a common vertical support. Queen Post Truss

The queen post truss, sometimes queenpost or queenspost, is similar to a king post truss in that the outer supports are angled towards the center of the structure. The primary difference is the horizontal extension at the centre which relies on beam action to provide mechanical stability. This truss style is only suitable for relatively short spans.

Lenticular Truss

American Lenticular Truss Bridges have the top and bottom chords of the truss arched forming a lens shape. Patented in 1878 by William Douglas.

Town's lattice truss

American architect Ithiel Town designed Town's Lattice Truss as an alternative to heavy-timber bridges. His design, patented in 1835, uses easy-to-handle planks arranged diagonally with short spaces in between them.

Vierendeel truss

The Vierendeel truss is a truss where the members are not triangulated but form rectangular openings, and is a frame with fixed joints that are capable of transferring and resisting bending moments. Regular trusses comprise members that are commonly assumed to have pinned joints with the implication that no moments exist at the jointed ends. This style of truss was named after the Belgian engineer Arthur Vierendeel, who developed the design in 1896. Its use for bridges is rare due to higher costs compared to a triangulated truss.

The utility of this type of truss in buildings is that there is no diagonal bracing, the creation of rectangular openings for windows and doors is simplified and in cases the need for compensating shear walls is reduced or eliminated.

After being damaged by the impact of a plane hitting the building, parts of the framed curtain walls of the Twin Towers of the World Trade Center resisted collapse by Vierendeel action displayed by the remaining portions of the frame.

Statics of trusses

A truss that is assumed to comprise members that are connected by means of pin joints, and which is supported at both ends by means of hinged joints or rollers, is described as being statically determinate. Newton's Laws apply to the structure as a whole, as well as to each node or joint. In order for any node that may be subject to an external load or force to remain static in space, the following conditions must hold: the sums of all horizontal forces, all vertical forces, as well as all moments acting about the node equal zero. Analysis of these conditions at each node yields the magnitude of the forces in each member of the truss. These may be compression or tension forces.

Forces in members

On the right is a simple, statically determinate flat truss with 9 joints and (2 x 9) − 3 = 15 members. External loads are concentrated in the outer joints. Since this is a symmetrical truss with symmetrical vertical loads, it is clear to see that the reactions at A and B are equal, vertical and half the total load.

The internal forces in the members of the truss can be calculated in a variety of ways including the graphical methods:

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